How do I delete a photo from my Mac?

It's a two step process:

In the Library select the image and hit the delete key, or right click on the image and select Delete 1 Photo

If you're viewing an image in an Album you can use command-delete

All of these do the same thing: move the image to the Recently Deleted folder. They will be deleted from there automatically within 30 days or so.

If you don't want to wait until then simply Right Click on the Recently Deleted icon on the left hand pane and choose Erase Deleted Items.